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MIT OpenCourseWareMIT 18.01SC Single Variable Calculus, Fall 2010 (2010)

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Instructors: Christine Breiner, David Jordan, Joel Lewis

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

View the complete course: http://ocw.mit.edu/18-01SCF10


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English
Keywords: recitations; differentiation of functions; integration of functions; limits; continuity; differentiation rules; extremum problems; definite integration; indefinite integration; fundamental theorem of calculus; techniques of integration; approximation of definite integrals; improper integrals; l'Hôpital's rule

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0


Individual Files

Movie Files MPEG4 Ogg Video
Recitation Introduction 3.5 MB 
5.8 MB 
Definition of the Derivative 27.2 MB 
49.6 MB 
Graphing a Derivative Function 26.3 MB 
42.0 MB 
Smoothing a Piece-wise Function 20.3 MB 
35.3 MB 
Constant Multiple Rule 15.5 MB 
29.6 MB 
Tangent Line to a Polynomial 10.8 MB 
20.1 MB 
Derivatives of Sine and Cosine 18.0 MB 
34.1 MB 
Product Rule 15.6 MB 
23.4 MB 
Quotient Rule 9.6 MB 
15.2 MB 
Chain Rule 17.0 MB 
26.7 MB 
Implicit Differentiation 18.2 MB 
34.0 MB 
Graphing the Arctan Function 9.6 MB 
18.1 MB 
Arccos 20.9 MB 
37.2 MB 
Log and Exponent Derivatives 15.5 MB 
24.5 MB 
Rules of Logs 20.1 MB 
33.6 MB 
Hyperbolic trig functions 29.2 MB 
53.7 MB 
Implicit differentiation and linear approximation 22.5 MB 
42.8 MB 
Quadratic Approximation 15.8 MB 
30.0 MB 
Quadratic Approximation of a Product 30.5 MB 
56.0 MB 
Sketching a curve 27.0 MB 
44.0 MB 
Closest Point to the Origin 14.5 MB 
20.8 MB 
Minimum Triangle Area 21.5 MB 
34.6 MB 
Maximum Surface Area 19.0 MB 
30.5 MB 
Related rates 1 17.2 MB 
31.4 MB 
Related rates 2 38.4 MB 
70.2 MB 
Using Newton's Method 16.9 MB 
26.3 MB 
Mean Value Theorem 13.3 MB 
21.1 MB 
Mean value theorem 7.4 MB 
12.5 MB 
Antidiff. With Discontinuity 19.5 MB 
37.1 MB 
Computing Differentials 8.9 MB 
15.2 MB 
Linear approx. with differentials 12.2 MB 
23.1 MB 
Computing Antiderivatives 19.5 MB 
36.9 MB 
Antidifferentiation by substitution 22.2 MB 
42.1 MB 
Differential Equation 7.5 MB 
11.3 MB 
Differential Equation With Graph 18.0 MB 
27.2 MB 
Summation Notation Practice 31.4 MB 
50.5 MB 
Riemann sum 16.4 MB 
26.8 MB 
Computing the Volume of a Paraboloid 15.6 MB 
25.0 MB 
4J3, Diffusion of a Chemical 26.9 MB 
48.4 MB 
Definite Integrals of tan(x) 13.4 MB 
25.5 MB 
Definite Integral by Substitution 21.1 MB 
40.3 MB 
Applying the Second Fundamental Theorem 9.4 MB 
15.3 MB 
Second fundamental theorem and chain rule 11.2 MB 
18.2 MB 
Second fundamental theorem and quadratic approximation 17.4 MB 
29.7 MB 
Area Between the Graphs of Sine and Cosine 8.8 MB 
16.5 MB 
Area Between y=x^3 and y=3x-2 19.4 MB 
35.9 MB 
Volume of a Paraboloid via Disks 13.1 MB 
21.6 MB 
Volume of Revolution via Shells 18.8 MB 
31.9 MB 
Average Velocity 16.1 MB 
30.8 MB 
Average x-Coordinate in a Region 23.4 MB 
44.8 MB 
Explanation of Simpson's rule 32.4 MB 
59.4 MB 
Using the Trapezoid and Simpson's rules 17.1 MB 
28.9 MB 
Trig Integral Practice 24.7 MB 
46.2 MB 
Trig Integrals and a Volume of Revolution 20.5 MB 
38.4 MB 
Integral of tan^4 (theta) 17.5 MB 
30.1 MB 
Hyperbolic Trig Sub 35.6 MB 
68.4 MB 
Integration by completing the square 31.0 MB 
52.4 MB 
Partial Fractions Decomposition 41.8 MB 
80.0 MB 
Finding u and v' When Integrating by Parts 25.5 MB 
38.7 MB 
Integrating sin^n(x) Using Reduction 36.9 MB 
69.8 MB 
Arc Length of y=x^(2/3) 15.4 MB 
29.4 MB 
Surface Area of a Torus 45.9 MB 
87.8 MB 
Parametric Arclength 19.4 MB 
36.9 MB 
Polar to Cartesian 19.0 MB 
29.7 MB 
Graph of r = 1 + cos(theta/2) 42.8 MB 
80.8 MB 
Integration Practice I 30.8 MB 
51.2 MB 
Integration Practice II 32.4 MB 
53.7 MB 
Integration Practice III 27.4 MB 
46.8 MB 
Integration Practice IV 39.5 MB 
76.5 MB 
l'Hospital Practice 23.4 MB 
45.0 MB 
Failure of L'Hospital's Rule 12.9 MB 
23.6 MB 
Indeterminate forms 25.5 MB 
48.4 MB 
A Solid With Finite Volume and Infinite Cross Section 13.2 MB 
21.5 MB 
Improper Integrals 43.1 MB 
64.5 MB 
Integral of x^n e^(-x) 23.4 MB 
41.1 MB 
Limit of a Series 10.9 MB 
18.7 MB 
Comparison Tests 33.1 MB 
62.7 MB 
Ratio Test for Convergence 29.6 MB 
55.0 MB 
Integral Test 17.1 MB 
29.4 MB 
Integral Test as Estimation 33.4 MB 
64.4 MB 
Ratio Test -- Radius of Convergence 39.5 MB 
70.8 MB 
Power Series Practice 21.9 MB 
41.3 MB 
Finding Taylor's Series 22.2 MB 
40.1 MB 
Taylor's Series of a Polynomial 15.5 MB 
29.1 MB 
Taylor's Series for sec(x) 25.4 MB 
46.6 MB 
Integration of Taylor's Series 17.2 MB 
27.7 MB 
Series Calculation Using a Riemann Sum 29.6 MB 
51.3 MB 
Image Files Thumbnail Animated GIF
Recitation Introduction 3.3 KB 
225.2 KB 
Definition of the Derivative 4.4 KB 
304.7 KB 
Graphing a Derivative Function 3.8 KB 
294.4 KB 
Smoothing a Piece-wise Function 4.6 KB 
232.5 KB 
Constant Multiple Rule 4.7 KB 
178.8 KB 
Tangent Line to a Polynomial 3.9 KB 
112.7 KB 
Derivatives of Sine and Cosine 4.2 KB 
209.8 KB 
Product Rule 3.9 KB 
164.6 KB 
Quotient Rule 3.9 KB 
99.6 KB 
Chain Rule 4.2 KB 
175.1 KB 
Implicit Differentiation 4.6 KB 
205.8 KB 
Graphing the Arctan Function 3.8 KB 
99.1 KB 
Arccos 3.7 KB 
232.0 KB 
Log and Exponent Derivatives 4.2 KB 
164.3 KB 
Rules of Logs 4.0 KB 
226.7 KB 
Hyperbolic trig functions 3.5 KB 
318.8 KB 
Implicit differentiation and linear approximation 3.8 KB 
238.0 KB 
Quadratic Approximation 4.7 KB 
173.0 KB 
Quadratic Approximation of a Product 4.9 KB 
358.6 KB 
Sketching a curve 4.0 KB 
296.8 KB 
Closest Point to the Origin 4.0 KB 
151.6 KB 
Minimum Triangle Area 3.3 KB 
221.2 KB 
Maximum Surface Area 4.0 KB 
200.5 KB 
Related rates 1 4.7 KB 
184.4 KB 
Related rates 2 4.1 KB 
213.3 KB 
Using Newton's Method 3.4 KB 
178.9 KB 
Mean Value Theorem 4.2 KB 
146.2 KB 
Mean value theorem 3.7 KB 
74.9 KB 
Antidiff. With Discontinuity 4.1 KB 
203.7 KB 
Computing Differentials 3.6 KB 
100.2 KB 
Linear approx. with differentials 4.9 KB 
139.4 KB 
Computing Antiderivatives 4.2 KB 
209.0 KB 
Antidifferentiation by substitution 4.5 KB 
242.6 KB 
Differential Equation 3.6 KB 
73.3 KB 
Differential Equation With Graph 4.3 KB 
187.1 KB 
Summation Notation Practice 3.6 KB 
339.8 KB 
Riemann sum 3.9 KB 
178.6 KB 
Computing the Volume of a Paraboloid 3.9 KB 
173.1 KB 
4J3, Diffusion of a Chemical 4.7 KB 
303.9 KB 
Definite Integrals of tan(x) 3.2 KB 
149.3 KB 
Definite Integral by Substitution 4.1 KB 
238.1 KB 
Applying the Second Fundamental Theorem 3.6 KB 
102.4 KB 
Second fundamental theorem and chain rule 4.1 KB 
118.8 KB 
Second fundamental theorem and quadratic approximation 4.4 KB 
184.6 KB 
Area Between the Graphs of Sine and Cosine 4.4 KB 
103.7 KB 
Area Between y=x^3 and y=3x-2 4.2 KB 
210.3 KB 
Volume of a Paraboloid via Disks 3.5 KB 
139.1 KB 
Volume of Revolution via Shells 4.3 KB 
210.0 KB 
Average Velocity 3.3 KB 
172.8 KB 
Average x-Coordinate in a Region 5.0 KB 
257.8 KB 
Explanation of Simpson's rule 5.1 KB 
366.6 KB 
Using the Trapezoid and Simpson's rules 4.5 KB 
189.6 KB 
Trig Integral Practice 3.6 KB 
280.4 KB 
Trig Integrals and a Volume of Revolution 3.5 KB 
224.7 KB 
Integral of tan^4 (theta) 3.3 KB 
199.5 KB 
Hyperbolic Trig Sub 4.6 KB 
208.7 KB 
Integration by completing the square 4.3 KB 
343.9 KB 
Partial Fractions Decomposition 4.2 KB 
239.3 KB 
Finding u and v' When Integrating by Parts 3.5 KB 
277.8 KB 
Integrating sin^n(x) Using Reduction 4.3 KB 
218.9 KB 
Arc Length of y=x^(2/3) 3.7 KB 
174.0 KB 
Surface Area of a Torus 4.2 KB 
262.6 KB 
Parametric Arclength 3.8 KB 
212.0 KB 
Polar to Cartesian 4.0 KB 
207.6 KB 
Graph of r = 1 + cos(theta/2) 5.6 KB 
234.9 KB 
Integration Practice I 4.0 KB 
335.5 KB 
Integration Practice II 3.9 KB 
343.3 KB 
Integration Practice III 4.0 KB 
281.2 KB 
Integration Practice IV 4.8 KB 
226.8 KB 
l'Hospital Practice 3.9 KB 
267.5 KB 
Failure of L'Hospital's Rule 4.4 KB 
135.3 KB 
Indeterminate forms 4.5 KB 
283.3 KB 
A Solid With Finite Volume and Infinite Cross Section 3.5 KB 
153.5 KB 
Improper Integrals 4.3 KB 
228.3 KB 
Integral of x^n e^(-x) 3.8 KB 
256.3 KB 
Limit of a Series 3.3 KB 
113.5 KB 
Comparison Tests 3.3 KB 
185.5 KB 
Ratio Test for Convergence 3.8 KB 
323.5 KB 
Integral Test 3.9 KB 
179.2 KB 
Integral Test as Estimation 3.9 KB 
187.9 KB 
Ratio Test -- Radius of Convergence 4.2 KB 
217.0 KB 
Power Series Practice 3.9 KB 
248.7 KB 
Finding Taylor's Series 3.0 KB 
240.1 KB 
Taylor's Series of a Polynomial 5.6 KB 
173.2 KB 
Taylor's Series for sec(x) 4.1 KB 
276.6 KB 
Integration of Taylor's Series 3.7 KB 
176.8 KB 
Series Calculation Using a Riemann Sum 4.0 KB 
317.8 KB 
Information FormatSize
MIT18_01SCF10_files.xml Metadata [file] 
MIT18_01SCF10_meta.xml Metadata 1.4 KB 
Other Files SubRip
Mean value theorem 5.3 KB 

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